An FIR under sections 354 (outraging woman's modesty), 323 (voluntary causing hurt) and 504 (intentional insult) of IPC was registered at the suburban Versova police station on the basis of the complaint, a senior police official said.
The model used to visit Mika's house often, he said.
However, denying the charge, Mika filed a counter-complaint later in the evening, saying the model was trying to extort money from him.
Mika told police the woman had demanded Rs five crore from him and threatened to ruin his career if he did not pay, but he refused.
No arrest has been made in the case.